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e63eb7f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | import OAI.Combinatorics.EditApproximation.Binary.BinaryCellGroupKernel
namespace OAI
/-! The cell kernel constructs its rational scales from the dyadic
parameter exponents. -/
namespace EditApproximation
namespace BinaryFraction
theorem computedGroupScales_value (M b F eM eb eF : ℕ)
(hM : M = 2 ^ eM) (hb : b = 2 ^ eb) (hF : F = 2 ^ eF) :
(groupScalesWithWork eM eb eF).1.map value = groupDyadicScales M b (nat F).value := by
rw [nat_value, hM, hb, hF, Nat.cast_pow, Nat.cast_ofNat]
exact groupScalesWithWork_value eM eb eF
def computedCellGroupWithWork {α : Type*} (source target : List α) {M : ℕ}
(parent : TargetInterval source.length) (b P F exponent Q eM eb eF : ℕ)
(hM : M = 2 ^ eM) (hb : b = 2 ^ eb) (hF : F = 2 ^ eF)
(tau a : BinaryFraction) (parentInitial : TargetInterval target.length → BinaryFraction)
(child initial current : Fin M → TargetInterval target.length → BinaryFraction)
(draw : cellScaleDraw M b Q (nat F).value) (cell : ℕ × ℕ) :
Option (BinaryBellmanAction (TargetInterval target.length)
(Fin M × TargetInterval target.length) M) × ℕ :=
let scales := groupScalesWithWork eM eb eF
let result := cellGroupWithWork source target parent b P F exponent Q
(by rw [hb]; exact Nat.two_pow_pos eb) tau a parentInitial child initial current scales.1
(computedGroupScales_value M b F eM eb eF hM hb hF) draw cell
(result.1, scales.2 + result.2 + 1)
theorem computedCellGroupWithWork_value {α : Type*} (source target : List α) {M : ℕ}
(parent : TargetInterval source.length) (b P F exponent Q eM eb eF : ℕ)
(hM : M = 2 ^ eM) (hb : b = 2 ^ eb) (hF : F = 2 ^ eF)
(tau a : BinaryFraction) (parentInitial : TargetInterval target.length → BinaryFraction)
(child initial current : Fin M → TargetInterval target.length → BinaryFraction)
(draw : cellScaleDraw M b Q (nat F).value) (cell : ℕ × ℕ) (hP : 0 < P) :
((computedCellGroupWithWork source target parent b P F exponent Q eM eb eF hM hb hF tau a
parentInitial child initial current draw cell).1.map BinaryBellmanAction.decode) =
chooseCellGroupAction source target parent b P F exponent Q tau.value a.value
(fun q => (parentInitial q).value) (fun i q => (child i q).value)
(fun i q => (initial i q).value) (fun i q => (current i q).value) cell
(Eq.mp (congrArg (cellScaleDraw M b Q) (nat_value F)) draw) := by
have h := cellGroupWithWork_value source target parent b P F exponent Q
(by rw [hb]; exact Nat.two_pow_pos eb) tau a parentInitial child initial current
(groupScalesWithWork eM eb eF).1 (computedGroupScales_value M b F eM eb eF hM hb hF)
draw cell hP
simpa only [computedCellGroupWithWork] using h
end BinaryFraction
end EditApproximation
end OAI
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